Seema Jangir, Gauree Shanker, Jaspreet Kaur, Laurian-Ioan Piscoran

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In this paper, we find a necessary and sufficient condition for a non-zero vector to be a geodesic vector in homogeneous generalized m-Kropina space. Further, we prove the existence of at least one homogeneous geodesic. However, it is conjectured that the outcomes and proofs in the case of Finsler geometry are not ideal, since general Finsler metrics are non-reversible. In Finsler geometry, the trajectory of unique homogeneous geodesic should be regarded as two geodesics with initial vectors X and -X. Hence, we construct an (n + 1)-dimensional and a 4-dimensional space to find homogeneous geodesics explicitly.


generalized m-Kropina space, Finsler geometry, homogeneous geodesic.

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DOI: https://doi.org/10.22190/FUMI230524020J


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